Start by preparing a pressure canner for hot pack based on the manufacturers instructions. That usually means adding in the bottom trivet, along with several inches of water and bring it to a simmer.
Prepare the soup for hot pack by chopping all ingredients. Peel and chop the carrots, dice the onions and celery.
Combine all ingredients in a large stock pot and bring the ingredients to a boil. Simmer for 5 to 10 minutes, until ingredients are heated through.
Use a slotted spoon to evenly distribute the solids among 4 quart jars or 8 pint jars.
Top with broth, leaving 1 inch headspace.
Cap with 2 part canning lids and process the jars in a pressure canner for 75 minutes for pints and 90 minutes for quarts, adjusting for altitude (see notes).
When the canning time is complete, allow the canner to cool to room temperature on it's own before removing the jars.
Check seals, and store any unsealed jars in the refrigerator for immediate use. Properly canned and sealed jars will maintain peak quality on the pantry shelf for 18 months, and be good to eat long after provided they're still sealed. Refrigerate after opening.
To serve, reheat in a saucepan and serve over cooked rice or pasta (or as is).